0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.13/0.33 % Computer : n016.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % WCLimit : 120 0.13/0.33 % DateTime : Thu Jul 2 07:50:50 EDT 2020 0.13/0.33 % CPUTime : 44.74/6.09 % SZS status Theorem 44.74/6.09 44.74/6.09 % SZS output start Proof 44.74/6.09 Take the following subset of the input axioms: 44.74/6.09 fof(fact_Lin__irrefl, axiom, ![V_L_2, V_ba_2, V_aa_2]: ((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_ba_2), V_aa_2)), V_L_2)) <= hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_aa_2), V_ba_2)), V_L_2))) <= hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), V_L_2), c_Arrow__Order__Mirabelle_OLin)))). 44.74/6.09 fof(fact_Nil2__notin__lex, axiom, ![V_xs_2, T_a, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_xs_2), c_List_Olist_ONil(T_a))), c_List_Olex(T_a, V_r_2)))). 44.74/6.09 fof(fact_Nil__notin__lex, axiom, ![V_ys_2, T_a, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), c_List_Olist_ONil(T_a)), V_ys_2)), c_List_Olex(T_a, V_r_2)))). 44.74/6.09 fof(fact_dropWhile__eq__Cons__conv, axiom, ![V_ys_2, V_y_2, V_xs_2, V_Pa_2, T_a]: ((V_xs_2=hAPP(hAPP(c_List_Oappend(T_a), c_List_OtakeWhile(T_a, V_Pa_2, V_xs_2)), hAPP(hAPP(c_List_Olist_OCons(T_a), V_y_2), V_ys_2)) & ~hBOOL(hAPP(V_Pa_2, V_y_2))) <=> c_List_OdropWhile(T_a, V_Pa_2, V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a), V_y_2), V_ys_2))). 44.74/6.09 fof(fact_ext, axiom, ![V_g_2, V_f_2]: (V_f_2=V_g_2 <= ![B_x]: hAPP(V_g_2, B_x)=hAPP(V_f_2, B_x))). 44.74/6.09 fof(fact_impossible__Cons, axiom, ![T_a, V_x, V_xs, V_ys]: (V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_ys) <= c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_List_Olist(T_a), V_xs), c_Nat_Osize__class_Osize(tc_List_Olist(T_a), V_ys)))). 44.74/6.10 fof(fact_in__measures_I1_J, axiom, ![V_y_2, T_a, V_x_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(T_a, T_a)), hAPP(hAPP(c_Product__Type_OPair(T_a, T_a), V_x_2), V_y_2)), c_List_Omeasures(T_a, c_List_Olist_ONil(tc_fun(T_a, tc_Nat_Onat)))))). 44.74/6.10 fof(fact_in__mkbot, axiom, ![V_y_2, V_z_2, V_L_2, V_x_2]: (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), c_Arrow__Order__Mirabelle_Omkbot(V_L_2, V_z_2))) <=> ((V_z_2=V_x_2 => V_y_2!=V_x_2) & ((V_z_2!=V_x_2 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), V_L_2))) & V_z_2!=V_y_2)))). 44.74/6.10 fof(fact_in__mktop, axiom, ![V_y_2, V_z_2, V_L_2, V_x_2]: (((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), V_L_2)) <= V_z_2!=V_y_2) & ((V_x_2!=V_y_2 <= V_y_2=V_z_2) & V_z_2!=V_x_2)) <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), c_Arrow__Order__Mirabelle_Omktop(V_L_2, V_z_2))))). 44.74/6.10 fof(fact_irrefl__def, axiom, ![T_a, V_r_2]: (c_Relation_Oirrefl(T_a, V_r_2) <=> ![B_x]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(T_a, T_a)), hAPP(hAPP(c_Product__Type_OPair(T_a, T_a), B_x), B_x)), V_r_2)))). 44.74/6.10 fof(fact_leD, axiom, ![T_a, V_x, V_y]: ((~c_Orderings_Oord__class_Oless(T_a, V_x, V_y) <= c_Orderings_Oord__class_Oless__eq(T_a, V_y, V_x)) <= class_Orderings_Olinorder(T_a))). 44.74/6.10 fof(fact_less__fun__def, axiom, ![T_a, V_g_2, V_f_2, T_b]: ((c_Orderings_Oord__class_Oless(tc_fun(T_a, T_b), V_f_2, V_g_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a, T_b), V_f_2, V_g_2) & ~c_Orderings_Oord__class_Oless__eq(tc_fun(T_a, T_b), V_g_2, V_f_2))) <= class_Orderings_Oord(T_b))). 44.74/6.10 fof(fact_less__imp__neq, axiom, ![T_a, V_x, V_y]: ((V_x!=V_y <= c_Orderings_Oord__class_Oless(T_a, V_x, V_y)) <= class_Orderings_Oorder(T_a))). 44.74/6.10 fof(fact_less__irrefl__nat, axiom, ![V_n]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_n)). 44.74/6.10 fof(fact_less__le__not__le, axiom, ![V_y_2, T_a, V_x_2]: (((~c_Orderings_Oord__class_Oless__eq(T_a, V_y_2, V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2)) <=> c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2)) <= class_Orderings_Opreorder(T_a))). 44.74/6.10 fof(fact_less__not__refl, axiom, ![V_n]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_n)). 44.74/6.10 fof(fact_less__not__refl2, axiom, ![V_m, V_n]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) => V_n!=V_m)). 44.74/6.10 fof(fact_less__not__refl3, axiom, ![V_s, V_t]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_s, V_t) => V_t!=V_s)). 44.74/6.10 fof(fact_lexord__Nil__right, axiom, ![T_a, V_r_2, V_x_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_x_2), c_List_Olist_ONil(T_a))), c_List_Olexord(T_a, V_r_2)))). 44.74/6.10 fof(fact_linorder__antisym__conv2, axiom, ![V_y_2, T_a, V_x_2]: (class_Orderings_Olinorder(T_a) => (c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2) => (V_y_2=V_x_2 <=> ~c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2))))). 44.74/6.10 fof(fact_linorder__neq__iff, axiom, ![V_y_2, T_a, V_x_2]: (class_Orderings_Olinorder(T_a) => (V_y_2!=V_x_2 <=> (c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2) | c_Orderings_Oord__class_Oless(T_a, V_y_2, V_x_2))))). 44.74/6.10 fof(fact_linorder__not__le, axiom, ![V_y_2, T_a, V_x_2]: (class_Orderings_Olinorder(T_a) => (~c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2) <=> c_Orderings_Oord__class_Oless(T_a, V_y_2, V_x_2)))). 44.74/6.10 fof(fact_linorder__not__less, axiom, ![V_y_2, T_a, V_x_2]: ((~c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2) <=> c_Orderings_Oord__class_Oless__eq(T_a, V_y_2, V_x_2)) <= class_Orderings_Olinorder(T_a))). 44.74/6.10 fof(fact_list_Osimps_I2_J, axiom, ![T_a, V_list_H, V_a_H]: c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_a_H), V_list_H)). 44.74/6.10 fof(fact_list_Osimps_I3_J, axiom, ![T_a, V_list_H, V_a_H]: hAPP(hAPP(c_List_Olist_OCons(T_a), V_a_H), V_list_H)!=c_List_Olist_ONil(T_a)). 44.74/6.10 fof(fact_nat__less__cases, axiom, ![V_Pa_2, V_n_2, V_m_2]: (((hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2)) <= (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2) => hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2)))) <= (V_n_2=V_m_2 => hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2)))) <= (hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2)) <= c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)))). 44.74/6.10 fof(fact_nat__less__le, axiom, ![V_n_2, V_m_2]: ((V_m_2!=V_n_2 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2))). 44.74/6.10 fof(fact_nat__neq__iff, axiom, ![V_n_2, V_m_2]: (V_m_2!=V_n_2 <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))). 44.74/6.10 fof(fact_not__Cons__self, axiom, ![T_a, V_x, V_xs]: hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs)!=V_xs). 44.74/6.10 fof(fact_not__Cons__self2, axiom, ![T_a, V_x, V_xs]: V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs)). 44.74/6.10 fof(fact_not__Nil__listrel1, axiom, ![V_xs_2, T_a, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), c_List_Olist_ONil(T_a)), V_xs_2)), c_List_Olistrel1(T_a, V_r_2)))). 44.74/6.10 fof(fact_not__less__iff__gr__or__eq, axiom, ![V_y_2, T_a, V_x_2]: (((V_x_2=V_y_2 | c_Orderings_Oord__class_Oless(T_a, V_y_2, V_x_2)) <=> ~c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2)) <= class_Orderings_Olinorder(T_a))). 44.74/6.10 fof(fact_not__listrel1__Nil, axiom, ![V_xs_2, T_a, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_xs_2), c_List_Olist_ONil(T_a))), c_List_Olistrel1(T_a, V_r_2)))). 44.74/6.10 fof(fact_nth__length__takeWhile, axiom, ![V_xs_2, V_Pa_2, T_a]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_List_Olist(T_a), c_List_OtakeWhile(T_a, V_Pa_2, V_xs_2)), c_Nat_Osize__class_Osize(tc_List_Olist(T_a), V_xs_2)) => ~hBOOL(hAPP(V_Pa_2, c_List_Onth(T_a, V_xs_2, c_Nat_Osize__class_Osize(tc_List_Olist(T_a), c_List_OtakeWhile(T_a, V_Pa_2, V_xs_2))))))). 44.74/6.10 fof(fact_order__less__asym, axiom, ![T_a, V_x, V_y]: ((c_Orderings_Oord__class_Oless(T_a, V_x, V_y) => ~c_Orderings_Oord__class_Oless(T_a, V_y, V_x)) <= class_Orderings_Opreorder(T_a))). 44.74/6.10 fof(fact_order__less__asym_H, axiom, ![T_a, V_a, V_b]: (class_Orderings_Opreorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_a, V_b) => ~c_Orderings_Oord__class_Oless(T_a, V_b, V_a)))). 44.74/6.10 fof(fact_order__less__imp__not__eq, axiom, ![T_a, V_x, V_y]: ((V_x!=V_y <= c_Orderings_Oord__class_Oless(T_a, V_x, V_y)) <= class_Orderings_Oorder(T_a))). 44.74/6.10 fof(fact_order__less__imp__not__eq2, axiom, ![T_a, V_x, V_y]: ((c_Orderings_Oord__class_Oless(T_a, V_x, V_y) => V_y!=V_x) <= class_Orderings_Oorder(T_a))). 44.74/6.10 fof(fact_order__less__imp__not__less, axiom, ![T_a, V_x, V_y]: ((~c_Orderings_Oord__class_Oless(T_a, V_y, V_x) <= c_Orderings_Oord__class_Oless(T_a, V_x, V_y)) <= class_Orderings_Opreorder(T_a))). 44.74/6.10 fof(fact_order__less__irrefl, axiom, ![T_a, V_x]: (~c_Orderings_Oord__class_Oless(T_a, V_x, V_x) <= class_Orderings_Opreorder(T_a))). 44.74/6.10 fof(fact_order__less__le, axiom, ![V_y_2, T_a, V_x_2]: (((V_x_2!=V_y_2 & c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2)) <=> c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2)) <= class_Orderings_Oorder(T_a))). 44.74/6.10 fof(fact_order__less__not__sym, axiom, ![T_a, V_x, V_y]: (class_Orderings_Opreorder(T_a) => (~c_Orderings_Oord__class_Oless(T_a, V_y, V_x) <= c_Orderings_Oord__class_Oless(T_a, V_x, V_y)))). 44.74/6.10 fof(fact_psubset__eq, axiom, ![T_a, V_A_2, V_B_2]: ((V_B_2!=V_A_2 & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a, tc_HOL_Obool), V_A_2, V_B_2)) <=> c_Orderings_Oord__class_Oless(tc_fun(T_a, tc_HOL_Obool), V_A_2, V_B_2))). 44.74/6.10 fof(fact_snoc__eq__iff__butlast, axiom, ![V_ys_2, V_xs_2, T_a, V_x_2]: (V_ys_2=hAPP(hAPP(c_List_Oappend(T_a), V_xs_2), hAPP(hAPP(c_List_Olist_OCons(T_a), V_x_2), c_List_Olist_ONil(T_a))) <=> (c_List_Obutlast(T_a, V_ys_2)=V_xs_2 & (c_List_Olast(T_a, V_ys_2)=V_x_2 & V_ys_2!=c_List_Olist_ONil(T_a))))). 44.74/6.10 fof(fact_xt1_I9_J, axiom, ![T_a, V_a, V_b]: ((~c_Orderings_Oord__class_Oless(T_a, V_a, V_b) <= c_Orderings_Oord__class_Oless(T_a, V_b, V_a)) <= class_Orderings_Oorder(T_a))). 44.74/6.10 fof(help_c__COMBI__1, axiom, ![T_a, V_P]: V_P=hAPP(c_COMBI(T_a), V_P)). 44.74/6.10 fof(help_c__COMBS__1, axiom, ![V_Pa_2, T_a, T_b, V_Q_2, V_R_2, T_c]: hAPP(hAPP(V_Pa_2, V_R_2), hAPP(V_Q_2, V_R_2))=hAPP(hAPP(hAPP(c_COMBS(T_b, T_c, T_a), V_Pa_2), V_Q_2), V_R_2)). 44.74/6.10 fof(help_c__fNot__1, axiom, ![V_Pa_2]: (~hBOOL(V_Pa_2) | ~hBOOL(hAPP(c_fNot, V_Pa_2)))). 44.74/6.10 44.74/6.10 Now clausify the problem and encode Horn clauses using encoding 3 of 44.74/6.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 44.74/6.10 We repeatedly replace C & s=t => u=v by the two clauses: 44.74/6.10 fresh(y, y, x1...xn) = u 44.74/6.10 C => fresh(s, t, x1...xn) = v 44.74/6.10 where fresh is a fresh function symbol and x1..xn are the free 44.74/6.10 variables of u and v. 44.74/6.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the 44.74/6.10 input problem has no model of domain size 1). 44.74/6.10 44.74/6.10 The encoding turns the above axioms into the following unit equations and goals: 44.74/6.10 44.74/6.10 Axiom 1 (help_c__COMBI__1): X = hAPP(c_COMBI(Y), X). 44.74/6.10 Axiom 2 (fact_ext): fresh7(hAPP(X, sK66_fact_ext_B_x(X, Y)), hAPP(Y, sK66_fact_ext_B_x(X, Y)), X, Y) = Y. 44.74/6.10 Axiom 3 (help_c__COMBS__1): hAPP(hAPP(X, Y), hAPP(Z, Y)) = hAPP(hAPP(hAPP(c_COMBS(W, V, U), X), Z), Y). 44.74/6.10 44.74/6.10 Lemma 4: fresh7(sK66_fact_ext_B_x(c_COMBI(X), Y), hAPP(Y, sK66_fact_ext_B_x(c_COMBI(X), Y)), c_COMBI(X), Y) = Y. 44.74/6.10 Proof: 44.74/6.10 fresh7(sK66_fact_ext_B_x(c_COMBI(X), Y), hAPP(Y, sK66_fact_ext_B_x(c_COMBI(X), Y)), c_COMBI(X), Y) 44.74/6.10 = { by axiom 1 (help_c__COMBI__1) } 44.74/6.10 fresh7(hAPP(c_COMBI(X), sK66_fact_ext_B_x(c_COMBI(X), Y)), hAPP(Y, sK66_fact_ext_B_x(c_COMBI(X), Y)), c_COMBI(X), Y) 44.74/6.10 = { by axiom 2 (fact_ext) } 44.74/6.10 Y 44.74/6.10 44.74/6.10 Goal 1 (fact_not__Cons__self2): X = hAPP(hAPP(c_List_Olist_OCons(Y), Z), X). 44.74/6.10 The goal is true when: 44.74/6.10 X = hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))) 44.74/6.10 Y = ? 44.74/6.10 Z = hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)) 44.74/6.10 where "?" stands for an arbitrary term of your choice. 44.74/6.10 44.74/6.10 Proof: 44.74/6.10 hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))) 44.74/6.10 = { by axiom 3 (help_c__COMBS__1) } 44.74/6.10 hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))), hAPP(c_COMBI(?), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)))) 44.74/6.10 = { by axiom 1 (help_c__COMBI__1) } 44.74/6.10 hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))) 44.74/6.10 = { by axiom 3 (help_c__COMBS__1) } 44.74/6.10 hAPP(hAPP(c_List_Olist_OCons(?), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))), hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)))) 44.74/6.10 % SZS output end Proof 44.74/6.10 44.74/6.10 RESULT: Theorem (the conjecture is true). 44.74/6.13 EOF